Remark 4.4 The concept of inner \(\alpha \) -thinness at infinity thus introduced actually coincides with that of \(\alpha \) -thinness at infinity, defined by T. Kurokawa and Y. Mizuta [1]}. To validate this claim, it is enough to show that the concept of capacity used in [1]} (see p. 534 for its definition) coincides with that of inner capacity, defined by (REF ); which however can be concluded from [3]}. Also observe that in the case where \(\alpha =2\)  and \(A\)  is Borel, the above concept of inner 2-thinness at infinity coincides with that of outer 2-thinness at infinity, introduced by J.L. Doob [4]}.

